On Parametric Gevrey Asymptotics for Singularly Perturbed Partial Differential Equations with Delays

Alberto Lastra and Stéphane Malek

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: We study a family of singularly perturbed q‐difference‐differential equations in the complex domain. We provide sectorial holomorphic solutions in the perturbation parameter ϵ. Moreover, we achieve the existence of a common formal power series in ϵ which represents each actual solution and establish q‐Gevrey estimates involved in this representation. The proof of the main result rests on a new version of the so‐called Malgrange‐Sibuya theorem regarding q‐Gevrey asymptotics. A particular Dirichlet like series is studied on the way.

Date: 2013
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https://doi.org/10.1155/2013/723040

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:723040

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